Norm conditions for uniform algebra isomorphisms

DOI10.2478/s11533-008-0016-xzbMath1151.46036OpenAlexW1994730147MaRDI QIDQ931590

Scott Lambert, Aaron Luttman

Publication date: 25 June 2008

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-008-0016-x

zbMATH Keywords

uniform algebrasperipheral spectrumisometric algebra isomorphism

Mathematics Subject Classification ID

Automatic continuity (46H40) Banach algebras of continuous functions, function algebras (46J10) Ideals, maximal ideals, boundaries (46J20)

Related Items

Almost weighted composition operators between Banach function algebras ⋮ Polynomially peripheral range-preserving maps between Banach algebras ⋮ Norm conditions for real-algebra isomorphisms between uniform algebras ⋮ Jordan product and local spectrum preservers ⋮ Nonlinear spectral radius preservers between certain non-unital Banach function algebras ⋮ Maps between Banach function algebras satisfying certain norm conditions ⋮ Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras ⋮ Maps between uniform algebras preserving norms of rational functions ⋮ Nonlinear maps preserving the reduced minimum modulus of operators ⋮ Almost composition operators between algebras of absolutely continuous functions ⋮ Banach function algebras and certain polynomially norm-preserving maps ⋮ Divisibly norm-preserving maps between commutative Banach algebras ⋮ Norm conditions on maps between certain subspaces of continuous functions ⋮ Generalized weak peripheral multiplicativity in algebras of Lipschitz functions ⋮ Peripheral local spectrum preservers of Jordan products of operators ⋮ Maps preserving the local spectrum of Jordan product of matrices ⋮ A generalization of the Banach-Stone theorem for commutative Banach algebras ⋮ Multiplicatively and non-symmetric multiplicatively norm-preserving maps ⋮ Generalizations of spectrally multiplicative surjections between uniform algebras ⋮ Nonlinear conditions for weighted composition operators between Lipschitz algebras ⋮ Nonlinear maps preserving the minimum and surjectivity moduli ⋮ A generalization of peripherally-multiplicative surjections between standard operator algebras ⋮ Maps which preserve norms of non-symmetrical quotients between groups of exponentials of Lipschitz functions

Cites Work

• Weakly peripherally multiplicative surjections of pointed Lipschitz algebras
• Norm-preserving surjections on algebras of continuous functions
• Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative
• Linear preserver problems: A brief introduction and some special techniques
• Some characterizations of the automorphisms of $B(H)$ and $C(X)$
• Multiplicatively spectrum-preserving maps of function algebras
• A characterization of multiplicative linear functionals in Banach algebras
• MULTIPLICATIVELY SPECTRUM-PRESERVING MAPS OF FUNCTION ALGEBRAS. II
• Uniform algebra isomorphisms and peripheral multiplicativity
• Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item